Real-normalized differentials with a single order 2 pole

A meromorphic differential on a Riemann surface is said to be {\it real-normalized} if all its periods are real. Real-normalized differentials surfaces of given genus with prescribed orders their poles form real orbifolds whose topology closely related that moduli spaces marked points. Our goal develop tools study this topology. We propose combinatorial model for the normalized single order $2$ pole and use it analyze corresponding absolute period foliation.